Numerical simulations of flow surrounding a synthetic jet actuating device are presented. By modifying a dynamic mesh technique available in OpenFOAM,a well-documented open-source solver for fluid dynamics, detailed computations of the sinusoidal motion of the synthetic jet diaphragm were possible. Numerical solutions were obtained by solving the two dimensional incompressible viscous N-S equations, with the use of a second order implicit time marching scheme and a central finite volume method for spatial discretization in both streamwise and crossflow directions. A systematic parameter study is reported here, in which the external Reynolds number, the diaphragm amplitude and frequency, and the slot dimensions are varied.